Chapter 6.3, Problem 1PSA

a

To determine

Indicate whether statement is true of false, if a plane contains one of the two skew lines, it contains the other.

Answer to Problem 1PSA

False, It will never contain the second skew line

Explanation of Solution

Given information:

A plane contains one of the two skew lines

Since, skew lines never intersect and are not parallel.

Hence, it will never contain the other

b

To determine

The following statement “The given line and given plane never meet, if they both are parallel” is true or not.

Answer to Problem 1PSA

True, The line and plane will never meet

Explanation of Solution

Given information:

The given and plane will never meet, if they are parallel

Parallel means never meet even on extension

c

To determine

Indicate whether statement is true of false, if two parallel lines are in different planes, the planes are parallel

Answer to Problem 1PSA

True but not always the given planes are parallel

Explanation of Solution

Given information:

Two lines are in different planes

Two planes are parallel, sometimes it parallel lines are lying in those planes

d

To determine

Indicate whether statement is true of false, the two planes are parallel, if a line is perpendicular to two planes.

Answer to Problem 1PSA

True, both the given planes will be parallel

Explanation of Solution

Given information:

A given line is perpendicular to two planes

The given line can be seen lying in two planes if both the given planes are parallel

e

To determine

Indicate whether statement is true of false, the given plane and line are parallel to each other, if a plane and a line not in the plane are each perpendicular to the same line

Answer to Problem 1PSA

True, they will be always parallel

Explanation of Solution

Given information:

The given plane and a line, not in the plane are each perpendicular to the same line parallel to each other

The given plane and a line which are not in the plane are each perpendicular to the same line is only possible when they are parallel to each other